Trans-Neptunian objects (TNOs) harbor pristine materials from the early solar system. The James Webb Space Telescope offers major insights into the spectral classification of these small bodies. Among the three major spectral classes of TNOs, "cliff" types exhibit steep, red slopes from 0.7 to 1.2 μm, sheer reflectance drops from 2.65 to 2.85 μm, and deep 3 μm absorptions with low reflectance longward of the band. These types show more features associated with simple hydrocarbons and methanol than other TNO types. Cliff-type spectra show two further spectral subclasses (hereafter Cliff1 and Cliff2 types), with all cold-classical TNOs exhibiting Cliff2-type spectra. We apply radiative-transfer-based spectral modeling from 2.0 to 3.6 μm for 16 cliff-type TNOs to quantify compositions and investigate depth dependencies, which is crucial for understanding the cliff type's role in the outer solar system's development. We find mixtures of methanol, water, and tholins/organics are primarily responsible for the prototypical 3 μm region of cliff-type spectra, with methanol and tholins/organics being particularly suggestive of distant formation. Our models also demonstrate Cliff1 and Cliff2 types have distinct compositions of higher methanol and tholin/organic abundances, respectively. We find the Mors-Somnus binary system to be compositionally homogenous, consistent with a formation scenario that sampled a similar region in the protoplanetary disk (i.e., streaming instability). Object 2004 PG115 is compositionally distinct from the rest of the cliff types, suggesting some objects have compositions intermediate between cliff subclasses and major TNO classes. Observations with higher spectral resolution and signal-to-noise ratio are crucial for better understanding minor, often aliphatic components of cliff-type spectra.